Construction of large sandwich structures

ABSTRACT

Composite metal panels comprise two parallel plates 1, 2 each laser-welded to an internally sandwiched corrugated stiffener plate 3. Typically, all the welds 6a, 6b are in the same sense; firstly, penetrating laser welds 6b are made along and through the troughs 5 of the corrugations into (or, less preferably, through) an underlying plate 2 and secondly welds 6a are made along and through an overlying plate 1 along and into or through the peaks of the corrugations 4. Such a panel can be readily fabricated into large-scale metal constructions, especially ships.

This invention relates to the construction of large sandwich metalstructures from plate material.

It has particular application to ship building, in which composite metalstructures incorporating metal plate are used in hull, superstructure,deckhouse, bulkhead or hatch fabrication etc, and accordingly theinvention will be described below primarily in such a context. However,the invention also has utility in respect of other structures such aslinkspans, bridges, oil rigs, offshore structures, platforms,containers, buildings, columns, pontoons, tubes, pipes, and like largewelded constructions.

In the construction of ships, the basic unit of the hull or bulkheadconstruction and other parts of ship construction is conventionally acomposite panel. Such a panel is typically made by (a) cutting up platematerial into predetermined sizes (b)butt-welding together the edges ofa number of such plates, and (c) applying stiffener bars parallel to (oracross) the butt welds. This forms a stiffened panel, stiffened by thebars which are of various cross sections but often rather L-shaped incross-section with a short foot portion integral with a long shankportion projecting from the panel. Such panels can be further fabricatedusing large dimension connecting webs welded to the plates at rightangles and/or parallel to the stiffeners, and possibly also mountinganother such stiffened plate opposed to the first to form a double skincompartment.

Conventionally a number of different weld techniques are used in thisconstruction such as butt welding, fillet welding, overhead welding andthe like. The process can moreover involve major lifting and turning ofthe panel during its construction and/or can involve the need forwelding operatives to work in confined internal spaces of a double skin.Our own earlier Patent Applications discuss weld techniques involvinglasers to rationalise and facilitate these known methods.

These earlier laser techniques were however confined to utilising lasersin such a way as to produce a composite article of more or lessconventional overall appearance (that is to say conventional apart fromdetails of the weld) which can be utilised as it stands in existingstructures.

We have now discovered a generally new construction of composite panel;methods for its fabrication; methods for its onward utilisation (that isto say, joining up with similar such composites); details of fixing,repair and transition techniques using such composites; and, in general,a new type of sandwich large-scale metal construction, especially ofship construction, using such a composite.

In one aspect the invention provides a ship or like large-scale metalconstruction in which structural, sub-dividing, or enclosing, hulls,bulkheads, deckhouses or like structures comprise composite metal panelsconsisting of two parallel plates secured to the peaks and troughsrespectively of a corrugated metal stiffener plate arranged between theparallel plates.

The type of structure defined above can be used alone, for example, forbulkheads, or like sub-division or cladding elements. However, two ormore such structures can themselves be linked together and form aparallel composite to define a hull compartment including sub-divisions.

In another aspect the invention comprises a composite metal panelcomprising two parallel plates secured to the peaks and troughsrespectively of a sandwiched corrugated metal stiffener plate by weldlines extending along the peaks and troughs.

Such a panel is a preferred constructional element of the shipconstruction and others as defined above.

Although the techniques of the invention can be used over a wide rangeof thicknesses, generally speaking plates from 1 to 25 millimetresthickness are envisaged for the component parts of the composite panelapplied to ships. For other applications greater thickness may berequired. It will be found usually preferable to have the two parallelplate portions each thicker than the metal thickness of the corrugatedplate portion.

The spacing of the corrugations (that is to say, the distance betweencorresponding points of one corrugation and the next) taken as a ratioto the separation of the parallel plates can vary again over wide rangesbut is preferably within the range of 1.5:1 to 1:1.5. More preferably itlies within a closer range, of 1.1:1 to 1:1.1, that is to say aboutunity from a production standpoint. Weight and strength considerationsin different applications may require a wider range of this ratio.

It is a preferable feature of the invention that the corrugated sheetbetween the panels has flat peaks and troughs. The external widthmeasurement of the flat peak where adopted is not limited but from aproduction standpoint preferably lies between the ranges of 1:3 to 1:7,that is to say, an average of about 1:5, in relation to the platespacing. Again, weight and strength considerations in differentapplications may require a wider range of this ratio. The area incontact of course will be narrower by virtue of the thickness of, andthe radius of any bend in, of the corrugated plate.

The weld lines fixing the parallel plates and corrugated plates togetherare most preferably those formed by laser through-welds, of the typeprovided by passing a high-intensity laser beam into or through bothlayers of metal and along the position of the peak or trough. Mostvaluably, the through welds are provided all in one sense, that is tosay so that successive welds pass through (a) trough material thensurface plate material and (b) plate material then peak material. Tofacilitate this, and as a further aspect of the invention a design ofplasma control device has been produced which will allow a gas-supplyingshoe into the valley of a corrugated profile to improve laserthrough-welding of the corrugated stiffener plate of the lower parallelplate. Such an arrangement, as described in more detail below, allows asingle weld orientation to be used and the avoidance of turning over ofthe composite panel structure halfway through its manufacture.

More particularly, the plate preferably has along one surface a numberof weld lines which pass through the surface plate and into anunderlying peak; and on the other surface no visible weld lines but aninternal weld line structure each line of which passes through a troughand into the material of the plate without however totally penetratingthat material. This gives a composite panel with weld lines on one facebut smooth surfaces on the other face. Of course, in a particularapplication it may be required that a weld should completely penetratethrough a facing plate.

The construction of the sandwich structure will not (in normal workshopor site conditions) prevent gaps occurring between, on the one hand, thetroughs and peaks of the corrugated plate, and, on the other, the faceplates. The preferred method of welding using a high-power density laserbeam also however allows the addition of material to run into and fillthe gaps between the plates making the sandwich panel. One method ofadding material to fill the gap is by wire feed. The addition of wirefeed also makes it possible to obtain a fine control over production asdescribed in our earlier Applications such as U.S. Patent applications601 424, 604 079 and other Applications equivalent to, or divided orcontinued from such Applications.

The product of the present invention is referred to as a sandwichcomposite panel of plate material. It is an understood terminology thatplate material, in the metallurgical art, is a thicker, denser and moredimensionally stable and stiff grade of material than sheet material.Typically plate thickness lies within the range of 1 to 25 millimetresas defined above, although in certain circumstances may extend above orbelow these limits.

Most typically, but not by way of limitation the sandwich composite isof a thickness such that the spacing between the external plates liesbetween 25 and 200 millimetres, more preferably between 50 and 150millimetres or, in a preferred standardised embodiment about 50 and 100millimetres. The surface plate in such an instance is between 5 and 15millimetres thick in typical embodiment, and the corrugated plate ispreferably similar and within the range of 2 to 10 millimetres thick.

The application of the invention to plate materials and minimisation ofthe use of rolled stiffener sections is of considerable importance.

It is known for example in aircraft construction to form a sandwichmaterial of thin lightweight metal sheet with corrugated metalreinforcement inside. Such material is normally made by electron beamwelding, but there has been a prior proposal to produce the material bya form of spot welding, known as pulse trains, using lasers. However,the overall composite product is very thin (the only example known is8.7 millimetres thick external dimensions) and is made of extremely thinsheet certainly not exceeding 1 mm in thickness. Also, it is alwayswelded by through welds from the outside inwards, in contrast to themuch preferred embodiment of the present invention which welds in onesense, that is to say alternately from the inside outwards and from theoutside inwards.

The present invention does not represent therefore a mere change ofscale as compared to the above invention. More specifically, thedifferences are

(a) A different type of welding in the prior art, that is to say spot(pulse train) welding as against continuous seam welding, also by asmall scale 300 w YAG laser as against a multi-kilowatt Co₂ laser,giving two-dimensional welding problems as against three-dimensional inthe large scale now proposed.

(b) Different weld directions on different faces in the presentinvention thus obviating the need to turn over the composite. This isparticular importance with a large scale fabrication and also permits adifferent design of the whole production line with consequent equipmentsavings

(c) A different field of eventual use in ships, buildings, offshorestructures, containers, platforms, linkspans, oil rigs, pipelines andother large scale users. The use of sandwich structures in ships etcresults in a superior end product from the aspects of weight, strength,headroom, damage from various causes, intactness, cleaning, painting,liquid flow and the transmission of vibration, heat and noise, etc.

(d) The design of joints between sandwich composite panels end-on,side-on, and perpendicular to one another.

(e) The use of sandwich structures in cylindrical or non-cylindricalarcuate shapes as against flat shapes.

(f) The design of penetrations and holes in sandwich structures.

(g) Repair procedures

(h) Protective measures against corrosion.

(i) The design of a laser-equipped sandwich panel line.

(j) Different characteristics of welding procedure including the use ofpaint-primed materials.

As to the last of these laser weld procedure depends upon the totalenergy input; extent and type of focusing; loss of metal if any byevaporation; plasma formation, or retention, or re-shaping; heatconduction away from the weld; surface tension of molten metal shape;and similar physical or chemical characteristics in the extremeconditions at the point of welding. Most if not all of these conditionsare not applicable in at all the same fashion in different scales ofworking. The Applicants have nonetheless found that through welding on aseam basis can be used and can be used moreover in either direction,that is to say, with the thick sheet before the thin sheet, or with thethin sheet before the thick sheet.

On the large scale it is not practical to depend upon the pressingtogether of flat plates and corrugated stiffener plate. Thethrough-welding procedure has been developed to cater for gaps betweenthese two component parts. A wire feed system is used to account forsuch gaps.

Moreover, an option in the finished product is of obtaining one surfacefree from weld lines and thus being particularly suitable to form theinner surface of containing tanks or holes, or the outer surface ofhulls.

In a further aspect welds can be made from inside the sandwich panel andthereby obtain two outer surfaces free from weld lines.

The invention will be further described with reference to theaccompanying drawings in which:

FIG. 1 is a cross-section through part of a composite double-skinnedpanel according to the invention,

FIGS. 2 and 2a show forms of transverse assembly of the composite ofFIG. 1, in perspective view,

FIG. 3 shows one form of longitudinal assembly of the composite of FIG.1, in perspective view.

FIG. 4 shows a perspective view of a preferred corner configuration ofthe panel facilitating fixing as in FIGS. 2 and 3,

FIG. 5 shows a flow sheet of a flat fabrication sequence,

FIG. 6 shows a diagram of one arrangement of a production line formaking such composites; in a particular application other designsolutions may be adopted.

FIG. 7 shows a hole for ducting or hatchway access formed through acomposite panel according to the present invention, and

FIG. 8 shows a laser-welded butt-through joint.

FIG. 1 shows a section through a portion of composite panel inaccordance with the invention. The composite panel comprises a top plate1, a bottom plate 2, and an internal corrugated plate 3, thecorrugations of which have, in the instance shown, flattened peaks andtroughs 4 and 5 respectively. The plates 1 and 2 are secured to thecorrugated plates 3 by laser through-welds referenced at 6a at the upperplate, and 6b at the lower plate. Such laser welds can be made by themethods described in our earlier patent Applications, namely bycontinuous tracking of for example a 10 kilowatt focussed laser beam. Asshown, the various welds 6 do not penetrate the underside of the lowerplate. It would appear that there is no loss in weld strength if theunderside is penetrated, but it is preferable if, at least for the lowerwelds 6b, complete penetration is avoided so that an unmarked surface isproVided on at least one side of the composite.

The composite as shown can readily be made by such welding withoutturning over, utilising the weld beam in a single vertical direction asshown by the arrows. To make such a composite, the lower plate 2 ispositioned as required, the corrugated plate 3 is placed upon it andwelded along each trough 5 to form the weld 6b, and the plate 1 isplaced over the corrugated plate and welded along each peak 4 to formthe weld 6a. Since the peaks and troughs are flat they readily lendthemselves to such welding, and since they are regularly spaced it issimple to arrange the laser welding head to follow the underlying courseof the fattened peak 4 even though the peak itself may be covered byplate 1.

The sandwich composite as shown can be made in a number of differentrelatively large scale sizes, and is not to be confused with the verythin metal skin, typically less than 10 millimetres in overallthickness, produced for aerospace purposes. Typically, the sandwichcomposite of the invention has an internal spacing dimension between theopposed inner faces of plates 1 and 2 of 50 or 100 millimetres, and acorrugation pitch of an equivalent amount, from, for example, the midpoints of each peak to the next peak. The thicknesses of plate can vary,as previously indicated, depending upon the strength of sandwichcomposite that is required. In the example the thicknesses are forplates 1 and 2 are 8 millimetres thick, and plate 3 is 3 millimetresthick.

FIGS. 2 and 2a shows methods of joining such a composite panel to anadjacent such panel by welding of a transverse connection. While severalmethods are possible, it has been found by the Applicants that one ofthe methods as shown is to be preferred.

With reference to FIG. 2, Alternative 1:-in this attachment procedure,composite panels A and B are utilised. As before, each possesses a topplate 1, a corrugated plate 3 and a lower plate 2. The end configurationof the panels will be apparent from FIG. 2, being such that thecorrugations 3 project by a distance (a) beyond the edge of plate 1, andthat plate 2 projects by a distance (b) beyond the ends of thecorrugations. The two panels A and B, of these particular endconfigurations, are united with the help of a corrugated insert C and aclosing plate D. The insert C has a total width of twice the distance(b) (minus any weld gap requirements) and is used to fill the gapbetween the ends of the corrugations of panels A and B. As shown indotted lines, backing corrugation strips (not shown) may be useddepending upon the welding process adopted. The closing plate D has atotal width of (2b+2a) (again, minus any weld gap requirements) and isused to fill the gap between two top plates on panels A and B. Theplates may have such edge preparations as necessary for the weldingprocess used.

To assemble two such panels, the first weld to be made would be thelower face plate butt weld one end of which is shown at 7, which can bedone by laser or by a conventional process such as a manual metal arc orsubmerged arc if necessary. The second welds to be made would be the twosets of butt welds between the corrugated plates 3 and insert C. Thefinal welds would be two further butt welds at 8 and 9 when the closingplate D is placed in position. If appropriate in a particularapplication laser welds could be incorporated along some or all of thepeaks and troughs of such an intermediate structure. In between thevarious welding operations the activities of cleaning, inspection andanti-corrosion treatment may be carried out as known per se.

With reference to FIG. 2a, Alternative 2, there is shown a second methodof joining such a composite panel to an adjacent such panel by thewelding in of a transverse connection.

In this attachment procedure composite panels A and B are utilised as inAlternative 1. The two panels A and B of this particular endconfiguration, are again united with the help of a corrugated insert C,closing plate D, but additionally stopper plates E1 and E2 are utilised.The stopper plates have a height equal to the depth of the corrugatedplate minus the thickness of the corrugated plate.

The insert C has a total width of twice the distance (b) minus twice thethickness of the stopper plate plus any gaps required by processes. Theclosing plate D has a total width (2b+2a) minus any gaps required byprocesses and is used to fill the gap between the two top plates onpanels A and B.

To assemble two such panels the first weld to be made would be the lowerface plate butt, one end of which is shown at 7, which can be done byhigh power density laser or conventional welding processes. The secondsubstantive welds to be made would be the two sets of butt welds betweenthe corrugated insert C and the stopper plates E1 and E2, which wouldhave been previously laser welded to the corrugated plate 3 during thefabrication sequence. The final welds would be two further butt welds at8 and 9 when the closing plate D is placed in position. If appropriatein a particular application laser welds could be incorporated along someor all of the peaks and troughs of such an intermediate structure.

In between the various welding operations the activities of cleaning,inspection and anti-corrosion may again be carried out.

FIG. 3 shows the joining of two composite panels A and B in alongitudinal manner. The procedure to make such a connection isconsiderably simpler than that for a transverse connection as shown inFIGS. 2 and 2a, the first weld being a butt weld 10 and the second weldbeing two similar butt welds 11 and 12 when the closing plate E is inposition. It will be apparent from FIG. 3 therefore, that both the upperand lower plates 1, 2 preferably terminate approximately halfway acrossa peak or trough respectively. The plates may have edge preparations asrequired by the welding processes.

FIG. 4 shows a corner of a composite panel in accordance with theinvention, showing a preferred configuration of upper and lower plates 1and 2, in relation to corrugated plate 3, at this location. As will beapparent from a consideration of FIGS. 2, and 2a and 3, it is preferredfor the top plate 1 to terminate at a distance (a) from the ends of thecorrugations, and for the bottom plate 2 to project for a distance (b)beyond such corrugations. It is also preferred, but not essential, forthe top plate 1 to finish approximately halfway across a peak 4, asshown and it is preferred for the bottom plate 2 to finish similarlyapproximatately halfway across a trough 5.

It will be appreciated therefore that a composite panel of the type ofcross-section generally as shown in FIG. 1, and having the cornerconfigurations generally as shown in FIG. 4, is a particular valuableembodiment of the present invention. It will also be appreciated thatAlternative 2 (FIG. 2a) simply adds a stopper plate to the end of thecorrugated plate 3.

FIG. 5 is a flow chart showing a typical composite sandwich panelfabrication sequence.

The example sequence shown is developed for the fabrication of astandard unit panel and is designed to permit a throughput capacity of acomposite panel at regular intervals using an appropriate laser powerper unit with sufficient units arranged as necessary.

The 3-millimetre and 8 millimetre plates are taken from the stock yard,levelled and cleaned. Following this stage they are sent on separatepaths. The 3-millimetre plate is sent to cold-rolling or other processfor formation of the necessary corrugations.

The 8-millimetre plate is cut to precise size and butt-welded to form apanel of plate. The panels are split into two streams. One face platepanel stream, destined to be the lower panel of plate, receives thecorrugated plate, and after tack welding is welded through the flattroughs of the corrugated plate to form the initial part of thecomposite. Butt through welds (see FIG. 8) may be required to joincorrugations to face plate if more than one corrugated plate is to beused, unless of course they are already welded together prior to fixingon the lower face plate. The other plate panel stream gives the otherplate panels which are positioned on top of the partly formed compositeand laser through-welded through the plate along the flattened peaks ofthe corrugations. This gives the complete composite panel. During orafter such fabrication various corrosion resistance measures may beapplied. Some of these may necessitate action prior to welding the upperface plate into position, and some after.

FIG. 6 shows diagrammatically a sample production line for such panels.Plates are butt welded into upper and lower panels at 13, held in abuffer store at 14, and then moved to weld station 15. Further panelsare also fed, to overlie the flat panels, from the corrugationgeneration equipment 16 via a buffer 17. The aligned corrugatedstiffeners are at this point held down on the underlying plate and thesubassembly laser welded in the troughs of the corrugations. Attentionis drawn to the projection of the lower plate beyond the end of thecorrugations, as shown in FIG. 4 above. The sub assembly moves toinspection 18. Top panels are then placed upon the corrugations (againto leave a certain proportion of corrugation projecting, as shown atstation 19) and welding is effected along the peaks through theuppermost plate panel. Finally, the assembly moves to inspection station20.

Provision is made, as shown in FIG. 6, for an overhead lifting facilityfor the individual panels and corrugated stiffening. Nonetheless, thisfacility can consist in a simple lifting and transfer arrangement, andit is not normally necessary to turn over the panels at any stage intheir fabrication. The whole sandwich line may be mechanised andautomated.

Attention is drawn to the laser beam ducts 21. In the practice of thisinvention, as described in their earlier Application, it is envisaged tohave a central laser generator and to transmit an unfocused laser beamdown a duct common to all of the processing installations, the beambeing selectively intercepted and thereafter directed along a duct on agantry to be focused by optics on to a workpiece.

FIG. 8 shows how a high power density laser beam may be used to producea weld which butts together two corrugated plates 3 whilst at the sametime creating a through connection between the corrugated plates 3 andthe lower face plate 2.

This joint configuration "Butt-through weld", may be used to joincorrugated plates in order to manufacture a sandwich compositestructure.

The composite panels made in accordance with the invention havegenerally smooth external surfaces, are smaller in overall thicknessdimension than existing forms of large structures, and in the endproduct i.e. ship or other are of considerably quicker fabrication timeand prime cost. In addition to these advantages, they are of a structureconsiderably simplified for cleaning and painting processes. Thus, theexternal surfaces are smooth apart from weld configurations and presentfewer problems of corrosion protection. Moreover, the internal surfacesare in effect simple polygonally sectioned tubed surfaces and can befilled with a paint or anti-corrosion material such as a foam, vapour,gas etc.

The type of composite panels shown can be used as it stands for the tanktop of a dry cargo ship, or for similar structures. In principle, thesandwich form could be applied to bottom shell, side shell decks,longitudinal bulkheads, transverse bulkheads, flats, platforms,superstructures, deck houses, etc. These main and minor structuralmembers may require further supporting members, in which case these maybe conventional stiffened webs or a second such sandwich panel structurespaced from the first. For example, initial studies have indicated thata flat 12 millimetre transverse floor structure supported by 180millimetre by 12 millimetre flat bars spaced at 600 millimetres could bereplaced by a 50 millimetre deep sandwich as shown comprising3-millimetre corrugated central plate welded between 6-millimetre faceplates.

Composite panels of the invention as shown could also be made to followa curved or part cylindrical path. This would require the production ofarcuate surface plates and the formation of the corrugated stiffenerplates to follow the same arcuate line. While the former plates arewithin the ambit of conventional fabrication techniques, the latterrepresent a less common fabrication, which may be carried out, forexample, by providing tapered corrugations and pressing them around aformer to give a conic development or by the use of tapered inserts.

FIG. 7 shows three assembled corrugated panels (the upper closing platesE of which have been omitted for clarity) provided at the fabricationstage with an elliptical access manhole 17. The side pieces of the mainpanel are indicated by reference letters a and c while the upper andlower semi-circular hole pieces are indicated by reference letters b andd. Such panels can be fabricated as necessary by a variant of theproduction line described above and be incorporated into the eventualstructure where desired. It is alternatively possible to providepostcutting of holes, since the structure is overall sufficiently rigidto withstand reasonable loss of integrity in this fashion.

I claim:
 1. A composite structure having a metal panel comprising firstand second parallel plates having opposing faces, a corrugated metalstiffener sandwiched between said plates and having a plurality ofparallel corrugations defining peaks and troughs, each corrugationhaving an end, said first and second plates being secured to the peaksand troughs, respectively, of said stiffener by weld lines extendingalong the peaks and troughs, said panel being assembled to a like panelwith the corrugations of both panels aligned end-to-end, with straightedges of said first plates opposing one another, and with straight edgesof said second plates opposing one another: wherein said straight edgeof each first plate extends parallel to and forwardly of a planecontaining the ends of the corrugations of the respective panel, andsaid straight edge of each second plate extends parallel to andrearwardly of said plane, and (a) a butt weld joins said first plateedges (b) a corrugated insert piece is joined at each of said opposingfaces by butt welds to the ends of the corrugations on the respectivepanels and (c) a plate insert is butt-welded at parallel edges thereofto said straight edges of said second plates.
 2. A panel assembly asclaimed in claim 1 in which said corrugated insert piece includes peaksand valleys, and welds along the peaks and valleys of said corrugatedinsert piece.
 3. A composite structure having a metal plane comprisingfirst and second parallel plates having opposing faces, a corrugatedmetal stiffener sandwiched between said plates and having a plurality ofparallel corrugations defining peaks and troughs, said first and secondplates being secured to the peaks and troughs, respectively, of saidstiffener by weld lines extending along the peaks and troughs, saidpanel being assembled to a like panel with straight edges of said firstplates opposed to one another and with straight edges of said secondplates opposed to one another, wherein opposed straight edges of saidfirst parallel plates are spaced forwardly of opposed straight edges ofsaid second parallel plates, and (a) a butt weld joins the firstparallel plate opposed edges (b) a plate insert is butt-welded atparallel edges thereof to the respective opposed straight edges of thesecond parallel plates.
 4. A composite metal panel having two faces andconsisting of:a first metal plate of at least 1 mm in thickness; astiffener plate of at least 1 mm in thickness, said stiffener platebeing configured with a plurality of parallel corrugations constitutingpeaks and troughs, wherein said corrugations have ends and each of saidpeaks and troughs has a center, said stiffener plate being welded to thefirst metal plate by laser welds extending along said troughs, throughthe thickness of the stiffener plate and into the first metal plate; anda second metal plate of at least 1 mm in thickness, said second metalplate also being welded to the stiffener plate by laser welds extendingin parallel lines along the second metal plate, through the thicknessthereof, and into and along said peaks of the stiffener plate; wherein(a) a straight end edge of said first plate is transverse to thecorrugations and is parallel to and spaced forwardly of a planecontaining the ends of the corrugations, and a straight end edge of saidsecond plate is transverse to the corrugations and is parallel to andspaced rearwardly of said plane and (b) another straight edge of saidfirst plate extends substantially along the center of a trough in acorrugation and another straight edge of said second plate extendssubstantially along the center of a peak in a corrugation.